Radial compression function for vector quantizer of Laplacian source with high dynamic variance range

Perić, Zoran; Jovanović, Aleksandra

doi:10.1002/ett.1463

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…If the fact that cells crossing lines s = r and s = − r (i.e. x 1 = 0 and x 2 = 0) are not quadratic is neglected, we can take the expression for D g ( Q 2 D ; σ ) given in :

{scriptD}_{g} ({scriptQ}^{2 D} MathClass-punc; σ) MathClass-rel= \frac{1}{24} {MathClass-op\sum}_{i MathClass-rel= 1}^{L} Δ_{i}^{2} P_{i}

where

\begin{matrix} aligned \\ right P_{i} = \int_{r_{i - 1}}^{r_{i}} p_{R} MathClass-open(r MathClass-close) dr & left = e^{- \frac{\sqrt{2} r_{i - 1}}{σ}} (\frac{\sqrt{2} r_{i - 1}}{σ} + 1) & right \\ right & left - e^{- \frac{\sqrt{2} r_{i}}{σ}} (\frac{\sqrt{2} r_{i}}{σ} + 1) . \end{matrix}

By direct computation, we obtain the closed‐form expressions for both overload distortions:

\begin{matrix} aligned \\ right D_{ol 1} (Q^{2 D}; σ) & left = \frac{r_{\max}}{24 \sqrt{2} σ} e^{- \frac{\sqrt{2} r_{\max}}{σ}} \end{matrix}

…”

Section: Two‐dimensional Radial Quantisation Of Laplacian Sourcementioning

confidence: 99%

“…If the fact that cells crossing lines s D r and s D r (i.e. x 1 D 0 and x 2 D 0) are not quadratic is neglected, we can take the expression for D g Q 2D I Á given in [13]:…”

Section: Two-dimensional Radial Quantisation Of Laplacian Sourcementioning

confidence: 99%

“…Encoding of an i th frame Require: Frame samples: x i;0 ; x i;1 ; : : : ; x i;M 1 . 1: Estimate frame variance i according to (13). 2: Quantise i using log-uniform quantiser defined by (14).…”

Section: Algorithmmentioning

confidence: 99%

“…The number of cells in each radial region are chosen so that all cells are quadratic. It is known that quadratic cells have minimal moment of inertia of all rectangular cells () and therefore provide minimal distortion.…”

Section: Introductionmentioning

confidence: 99%

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Two‐dimensional radial μ‐law companding quantiser for Laplacian source

Perić

Petković

2013

Trans. Emerging Tel. Tech.

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This paper provides analysis of two‐dimensional radial μ‐law companding quantiser for quantisation and coding of a signal that has Laplacian distribution. Closed‐form expressions are obtained, both for the distortion and the bitrate of an output signal. An approximate expression for the required number of radial levels is also given, as well as an algorithm for computing its exact value. Complete procedure is demonstrated on a few numerical examples, and a comparison is performed with classical scalar μ‐law companding quantiser. It is shown that our model improves maximal SQNR value for 3.5 dB, and has narrower characteristics in a wide range of input signal power. Among many others, the application in the speech coding is described in details.Copyright © 2013 John Wiley & Sons, Ltd.

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“…If the fact that cells crossing lines s = r and s = − r (i.e. x 1 = 0 and x 2 = 0) are not quadratic is neglected, we can take the expression for D g ( Q 2 D ; σ ) given in :

{scriptD}_{g} ({scriptQ}^{2 D} MathClass-punc; σ) MathClass-rel= \frac{1}{24} {MathClass-op\sum}_{i MathClass-rel= 1}^{L} Δ_{i}^{2} P_{i}

where

\begin{matrix} aligned \\ right P_{i} = \int_{r_{i - 1}}^{r_{i}} p_{R} MathClass-open(r MathClass-close) dr & left = e^{- \frac{\sqrt{2} r_{i - 1}}{σ}} (\frac{\sqrt{2} r_{i - 1}}{σ} + 1) & right \\ right & left - e^{- \frac{\sqrt{2} r_{i}}{σ}} (\frac{\sqrt{2} r_{i}}{σ} + 1) . \end{matrix}

By direct computation, we obtain the closed‐form expressions for both overload distortions:

\begin{matrix} aligned \\ right D_{ol 1} (Q^{2 D}; σ) & left = \frac{r_{\max}}{24 \sqrt{2} σ} e^{- \frac{\sqrt{2} r_{\max}}{σ}} \end{matrix}

…”

Section: Two‐dimensional Radial Quantisation Of Laplacian Sourcementioning

confidence: 99%

“…If the fact that cells crossing lines s D r and s D r (i.e. x 1 D 0 and x 2 D 0) are not quadratic is neglected, we can take the expression for D g Q 2D I Á given in [13]:…”

Section: Two-dimensional Radial Quantisation Of Laplacian Sourcementioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two‐dimensional radial μ‐law companding quantiser for Laplacian source

Perić

Petković

2013

Trans. Emerging Tel. Tech.

Self Cite

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“…The best way to reduce the bit rate without affecting the quantization quality is the use of vector quantization (VQ) [27][28][29][30][31].…”

Section: Performance Of the Differential Scalar Quantizationmentioning

confidence: 99%

Intraframe quantization of speech line spectrum pairs for code‐excited linear prediction based coders in packet networks

Merazka

2012

Trans. Emerging Tel. Tech.

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This paper proposes intraframe quantization schemes of line spectrum pair parameters to improve frame erasures for the ITU‐T G.723.1 coder. The standard ITU‐T G.723.1 coder uses an interframe quantization of the line spectrum pair parameters, which causes error propagation to the next frames. Simulation results show that our intraframe quantization schemes coding is much more robust to frame erasures than the embedded method in ITU‐T G.723.1, and a typical improvement of 0.4 dB on average spectral distortion can be obtained with 40% packet loss. Enhanced modified bark spectral distortion tests, under various packet loss conditions, confirm that our proposed method is superior to the interframe algorithm embedded in the ITU‐T G.723.1 coder of over 1.6. Copyright © 2012 John Wiley & Sons, Ltd.

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